Set up an Euler's method spreadsheet for each of the following systems:
(a) Example 5 (b) Example 6 (c) Example 9 Choose an initial condition that corresponds to Fig. 6. 1. l, 6.1.2, or 6. I. 7 as appropriate. use a step size h = 0. 1, and confirm that the solutions indeed set off in the directions shown in the figures. If you go far enough, you may see a gradual divergence from the pictured solutions, which were calculated by a fancier method (Runge-Kutta) that pro-­ vides good accuracy with fewer steps than Euler's method. Describe any such observations.
Finding Trajectories I/ the first-order equation

Can be solved for y as a function of x., the graph of such a function is a phase -plane trajectory for the system
x' = ax +by.
y' = cx+ dy.
Altemathely, one may obtain trajectories by solving

For x as function of y. Use one or both of these techn9iques to determine and sketch phase -plane trajectories for the systems of problems 13 and 14. Predict how the speed of a point trav-eling along a trajectory will be affected by the position of the point.

Transcribed Image Text:

8 dx ax + by dr ax +by c.r